Title: Modeling and topological methods to better understand pattern formation in fish

Abstract: Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, voters in an election, or locusts in a swarm. Self-organization also occurs at much smaller scales in biology, though, and here I will focus on elucidating how brightly colored cells interact to form skin patterns in zebrafish. Wild-type zebrafish are named for their dark and light stripes, but mutant zebrafish feature variable skin patterns, including spots and labyrinth curves. All these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells. This leads to the question: how do cell interactions change to create mutant patterns? The longterm motivation for my work is to help shed light on this question and better link genes, cell behavior, and visible animal characteristics. Toward this goal, we combine different modeling approaches (including agent-based and continuum) to simulate pattern formation and make experimentally testable predictions. In this talk, I will overview our models and highlight how topological data analysis can be used to quantitatively describe self-organization in silico and in vivo.